We calculate the decay η3π at next-to-next-to-leading order or order p⁶ in Chiral Perturbation Theory. The corrections are somewhat larger than was indicated by dispersive estimates. We present numerical results for the Dalitz plot parameters, the ratio r of the neutral to charged decay and the total decay rate. In addition we derive an inequality between the slope parameters of the charged and neutral decay. The experimental charged decay rate leads to central values for the isospin breaking quantities R = 42.2 and Q = 23.2.